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saw5 [17]
2 years ago
8

The area of a quadrilateral whose vertices is ABCD taken in order are (1,2) (-5,6) (7,-4) and (-2,t) be 0 ,find the value of t

Mathematics
1 answer:
AfilCa [17]2 years ago
3 0
Coordinates : A(1,2) B(-5,6) C(7,-4) D(-2,t) - All are taken in order

gradient of AB = (6-2)/(-5-1) = 4/-6 = -⅔
since it is quadrilateral, AB//CD
gradient of CD = -⅔
equation of CD : y-(-4)=-⅔(x-7)
y+4=-⅔x+14/3
y=-⅔x+⅔
now, sub x=-2 from D(-2,t)
since t is the y-coordinate of point D
t=-⅔(-2)+⅔
t=2

Therefore, t=2
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Write the linear equation that gives the rule for this table.
Maksim231197 [3]

to get the equation of any straight line all we need is two points, well, let's just grab them from the table.

hmmm let's use (-49 , -39) and hmmm say (67 , 77)

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\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-39)}=\stackrel{m}{1}(x-\stackrel{x_1}{(-49)}) \\\\\\ y+39=1(x+49)\implies y+39=x+49\implies y=x+10

8 0
3 years ago
The sum of a number and three is doubled and then added to the product of six and the original number to give forty six
Zina [86]

Answer:

The number is 5

Step-by-step explanation:

Let x represent the number

Now let's break it down!

Sum of a number and 3 gives;

x + 3

This is then doubled to give;

2* (x + 3)

This is added to the product of 6 and the original number to give 46

Product of 6 and the original number = 6 * x

Now 2* (x + 3) is added to 6 * x to give 46

2* (x + 3) + 6*x = 46

2x + 6 + 6x = 46

8x + 6 = 46

Subtract 6 from both sides

8x + 6 - 6 = 46 - 6

8x = 40

x = 40/8

x = 5

Hence, the number is 5

3 0
3 years ago
Help me please !!!
Nat2105 [25]

Answer:

For 3x^2+4x+4=0

Discriminant= = -32

The solutions are

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= -44

The solutions

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= -36

The solutions

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a= (1-√-1)/3

Step-by-step explanation:

Formula for the discriminant = b²-4ac

let the discriminant be = x for the equations

The solution of the equations

= (-b+√x)/2a and = (-b-√x)/2a

For 3x^2+4x+4=0

Discriminant= 4²-4(3)(4)

Discriminant= 16-48

Discriminant= = -32

The solutions

(-b+√x)/2a =( -4+√-32)/6

(-b+√x)/2a= (-4 +4√-2)/6

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a =( -4-√-32)/6

(-b-√x)/2a= (-4 -4√-2)/6

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= 2²-4(3)(4)

Discriminant= 4-48

Discriminant= -44

The solutions

(-b+√x)/2a =( -2+√-44)/6

(-b+√x)/2a= (-2 +2√-11)/6

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a =( -2-√-44)/6

(-b-√x)/2a= (-2 -2√-11)/6

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= (-6)²-4(9)(2)

Discriminant= 36 -72

Discriminant= -36

The solutions

(-b+√x)/2a =( 6+√-36)/18

(-b+√x)/2a= (6 +6√-1)/18

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a =( 6-√-36)/18

(-b-√x)/2a= (6 -6√-1)/18

(-b-√x)/2a= (1-√-1)/3

6 0
4 years ago
In a bag there are 4 purple marbles, 3 green marbles, and 10 yellow marbles. If a student draws one marble what is the sample sp
guajiro [1.7K]
The correct answer Is D. Purple , Green , Yellow 

Hope I helped! ( Smiles )
6 0
3 years ago
Can someone help me with this math? I'd be glad to help you with something you need.
mr_godi [17]

Answer:

I believe it would be A bc

Step-by-step explanation:

A= 42

B= 32

C= 20

D= 36

5 0
3 years ago
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